Sensitivity, Specificity, and Receiver- Operator Characteristic Curves 10/10/2013

Definition Sensitivity: the fraction of all those with the disease who get a positive test result. C/(C+D) Specificity: the fraction of those without the disease who get a negative test result. B/(B+A) Positive predictive value: True positives/All positive results, C/(A+C) Negative predictive value: True negatives/All negative results, B/(B+D) DECISION: ABNORMAL DECISION: NORMAL TEST RESULT TEST RESULT TOTAL Disease absent A B A+B Disease present C D C+D Total A+C B+D A+B+C+D False positive False negative True negative True positive False-positive and false-negative lab results are similar to Type1 and Type II errors in statistical hypothesis testing. DECISION: REJECT DECISION: DO NOT REGECT NULL HYPOTHESIS NULL HYPOTHESIS Null hypothesis is true Type I error Null hypothesis is false Type II error

DECISION:ABNORMAL DECISION: NORMAL TEST RESULT TEST RESULT TOTAL Disease absent 36, , ,900 Disease present Total 37, ,000,000 Expected results of resulting one million people with porphyria test from a population with a prevalence of 0.01%. 82% of patients with porphyria have an abnormal test result; 3.7% of normal people have an abnormal test result. What is the likelihood that a patient has porphyria? (Or positive predictive value) The lower the prevalence of the disease, the lower the ratio of true positives to false positives. 82/37078≈0.002

Relationships between sensitivity and power and specificity and alpha Power or Sensitivity Specificity

Receive Operator Characteristic Curves (ROC) Threshold high low Sensitivity Specificity Sensitivity Specificity Tradeoff between sensitivity and specificity in one diagnostic test The threshold can help to separate a clinical diagnosis of normal from one of abnormal Optimal threshold, how to find? If interested, Please search it on the internet.

Interpreting clinical laboratory tests: One condition: what you know about the clinical context Another condition: what you learn from the lab test

Bayes, Genetic Linkage and Log of Odds (LOD)scores Why do geneticists usually conclude on studies of linkage: if a LOD score equals or exceeds 3, the marker and disease are considered to be linked? if a LOD score is less than or equal to -2, the marker and disease are not linked ? if a LOD score is between -2 and 3, the evidence is not conclusive ? Using Bayesian logic: Posttest odds of linkage=pretest odds of linkage. Likelihood ratio (1)Common definitions of linkage, 2% of randomly selected marker are linked to any particular disease gene. So odds=2%/(1-2%) ≈ (2)If a LOD score=3, converting likelihood ratio=10^3 =1000 (3) The posttest odds of linkage=0.02X1000=20 (4) Converting to possibility =20/(1+20)=20/21≈0.95, that is to say, the probability that the marker and disease are truly linked 95%. There is 95% chance that you will be correct, leaving a 5%chance that you will be wrong